Screening generally doesn't affect the fetus and can help make a decision about whether or not to do a more invasive test in the absence of other risk factors. Most screening is also before the timeframe that you're able to perform something like amniocentesis. Thinking PGD (for IVF), NIPT, NT ultrasound, serum screening, other such things...

I don't know a lot of people that refuse the noninvasive prenatal screening offered by California... even if you don't act on the information you receive.